Optimizing Precision in Geodetic Surveying: Insights from GNSS Post processing

1.    INTRODUCTION

The intended output of the study was to investigate the impact of GPS session time (T) and baseline length (D) on the precision. Further, it was planned to compare the precision of post possessing using broadcast ephemeris and rapid ephemeris data. In order to achieve the aforesaid requirements separate GPS static observation sessions were planned using two Trimble R7 receivers set installed at HM school rooftop. One receiver (Rx 1 - Roof 1) collects data with different time duration ranging from 1 min to 6 hours and the other receiver (Rx 2 - Roof 2) session continues for 24hrs. On the same day, Rx 1 data post-processed connecting baseline to PHTH (Plymouth OS Net) and TAUO (Tauoton OS Net) using broadcast ephemeris to investigate the quality of the derived positions for the different time interval. Considering the distance between Rx 1 - PHTH (short baseline < 5Km) and Rx 1 – TUAO (Long baseline c 100Km) investigate the quality of the derived positions, thence investigate the accuracy with the baseline length. Corresponding rapid ephemeris data downloaded for GPS satellite constellation. Receiver 2 (Rx 2) continue for 40hrs observation data then processed through TBC with broadcast and rapid ephemeris connecting as single baseline each to five different reference stations from Ordinance Survey Network (OS Net) with different distances ranging 4km to 1000km to investigate the quality of derived positions with regard to different ephemeris. This report has subdivided into three sections to present the finding in brevity. The first section will address derived positional quality on the GPS session time (T) and next on baseline length (D).  In the last section, post possessing using broadcast ephemeris and rapid ephemeris (E) will analyze.

A.           SESSION TIME (T) VS PRECISION                                                               

The aim of this investigation is to determine is there any relationship between session time (T) of GNSS data collected and precision of the derived position/ coordinates. Time constrain is a vital fact for the military hence it is important to study the minimum time taken to achieve the point of diminishing return of precision of any survey works. This would limit by various factors; limitation of the equipment, limitation of processing and geometry of satellite constellations, etc. However, it was assumed that all other factors were kept identical for all observations and only the session time changed in order to investigate the relationship between session time and precision.

i.      HYPOTHESIS

 The precision of the derived position will increase with increasing session time, which will limit by other factors and continue with a point of diminishing return.

 ii.     METHODOLOGY         

GPS observations session planned in a different time interval as given study setup and 30-second epoch static observation carried out. In every observation throughout the study, the receiver epoch was set to 30 seconds to maintain the same epoch with reference stations in OS Net. The cutoff angle of the receiver was set to 15 degrees to minimize tropospheric refractions and to maintain satellite geometry optimally. Receiver 1 (Trimble R7) installed in HM school (Antenna at rooftop) collect the data for the following discrete interval; 1, 2, 5, 10, 20, 30 min, and 1, 2, and 6 hours. However, 5 min observation revealed that it took 6 min of observation but the post-processing continue as it is. Then data processed with PHTH (OS Net) reference station and broadcast ephemeris for the corresponding time downloaded from OS Net.

TBC v 5.30 version used to process the data and accepted criteria (Chart 01) were defined as indicated in SOPs. Followed SOP's mostly compatible with TBC v 4 and for the same reason as v 5.30 adopt different time interval for computations according to the observation time we had to defined and force the software to calculate time interval for 30 sec as we set epoch.   

                                                            Flag                                         Fail

Horizontal Precision              0.020m + 1.0 ppm                  0.050m + 1.0 ppm

Vertical Precision                   0.020m + 1.0 ppm                  0.050m + 1.0 ppm

  Accepted criteria

It was also set up to give a fix solution and processing interval set to 30 sec. Processed with the broadcast ephemeris and throughout the study, this basic setup for the Trimble Business Centre v 5.30 was used (Except the post-processing of rapid ephemeris). The reference station used for post-processing was PHTH (OS Net) as the nearest OS Net station to HM school. However, the precision of the reference station as indicated in OS Net generally better than 0.008m (Horizontal 0.8cm) and 0.020m (Vertical 2.0cm). Hence it can be assured that the accuracy of derived coordinates will never get the accuracy than the reference stations.

Post-processed reports for all the observations analyzed and horizontal precision, vertical precision and combine precision used to compare the results for different session times. The assumptions were made as all the observations are post processed with PHTH reference station, all the observations made within daylight in 2 days, same receiver (and Antenna) used for all observations and processing done with the same software. Hence most of the other factor affecting the precision of observations are constant (However it is understood that those factors are not the same and anomalies will be discussed in a separate section)

 iii.      RESULTS

The below chart (Chart 02) shows the precision of the derived position of antenna 1. Further graphic representation (Graph 01) of the same data set shows the general trend line (Relationship) for the session time and precision of derived coordinates.

Most of the data gathered on 30 November and only the 6-hour data gathered on 01 December. All the data gathered in daylight and forenoon hours of both days. 30 November was a fair day with clear skies and Relative Humidity was (RH) 88%, while 01st of December morning hours partly cloudy and become clear and fair by noon RH 86-61%. Same weather condition expected in both receiver and reference station as the distance between two is about 4Km.

iv.      DISCUSSION OF SESSION LENGTH AND RESULTS

All the solutions were fixed and when investigating the horizontal, vertical, and combine precision it shows that there is a positive relationship between precision and session time. More session time for the observation gave high precision in derived coordinates. However, the first observation (1min) showing a high precision than that of 2 min. But investigating the epoch shows that it has 3 epoch (30sec x 3) for that particular observation. Further PDOP value also better than that of 2 min observation which makes good geometry for the calculations. These can conclude 1min observation better than 2 min and that is an exception but except 1 min observation, the general trend of the graph shows a clear relationship with time and precision of derived coordinates. Hence our hypothesis was proven and that can be generalized; the precision of derived coordinates increase with session time and after about 1 Hrs it comes to the diminishing of return                                               

iv.     PROBLEMS ENCOUNTER AND ANOMALIES  

Using the double differencing technique 98% of ionosphere bias mitigate. Hence we consider the ionosphere effect for our study is very less whereas the troposphere delays could make significant differences in respective precisions. However, to mitigate this bias tropospheric models such as Hopfield tropospheric models are used in post-processing. Even in these models, by assuming a change in pressure of 0.119 mill bars per metre of altitude difference. Ultimately, the tropospheric delay is defined as a function of height and the effect of pseudo rage given in meters with respect to the height of the troposphere. Hence it is critical to measure the height of the receiver and the elevation or height difference of receiver and reference station which will directly affect the precision of the derived coordinates. Elevation gained 105m in reference station at PHTH might affect the precision in great portion however, in our study, we considered for all our observations that affect equally where our final goal was to analyze the precision against session time. Moreover, the 'wet' component, which is a function of the water vapor and condensed water in form of clouds and, thence, it depends on weather conditions. The delay is small in this case, only some tens of centimeters, but this component varies faster than the hydrostatic component and a quite random way, being very difficult to model. Hence the observation of weather and humidity can predict the quality of the observations in respective reference stations and receivers. 20 min observation shows the poor precision and observation taken from 1327hrs to 1347 hours and the weather on the same day noon was mostly cloudy and becoming overcast RH 93%. This could have affected the precision of 20min observation.

 v.        RECOMMENDATIONS AND FURTHER INVESTIGATION

Highly recommend to use the techniques and criteria for the TBC or any software with updated SOP's and it is to be noted that TBC v 5.30 change the processing interval according to the session length of observations. It also recommends for future surveyors to carry out the same observation at the same timing on different days having 4 min gap to catch the same GPS constellation. 

B.  LENGTH OF BASELINE VS PRECISION

This investigation is to determine if there is a relationship between the baseline length and precision of derived coordinates. Different geographical locations compared to the distance between satellite and receiver will be affected by satellite geometry and different satellite will be observed at the same time. Hence the increase of the distance between the reference station and receiver will result in a decrease in precision of the derived position. However, more closely the reference station will increase the accuracy with the diminishing of return with the influence of other factors. 

i.     HYPOTHESIS                                                               

An increase in baseline length will decrease the precision of derived position coordinates. Hence the baseline length and accuracy will have a negative relationship.

ii.     METHODOLOGY                                                                                             

Same observations data gathered in the previous session used, yet this time all the data reprocessed with another reference station at about 100Km away from the receiver 1. TAUO (Taunton OS Net) station observed ephemeris used to re-process the same set of data and consider it as a long baseline (100Km) and previously processed results consider as a short baseline (5Km). The same basic setup for the Trimble Business Centre used as in the previous section and combine the precision of both the derived coordinates were used to analyze the relationship.

iii.      RESULTS

The results of obtained positioning accuracy based on session length are presented in this section. The following figures and tables are presented to provide some insight into the accuracy of the derived coordinates from different baseline lengths (Short baseline and long-baseline)

Comparison of combined precision of both results shows how the distance between receiver and reference station effect on the precision of derived coordinate.

The following graph shows the relationship of combined precisions of respective observation with a short baseline and long baseline.

iv.      DISCUSSION OF BASELINE LENGTH AND PRECISION

First of all by investigating the result of post-processed data with TAUO it supports the first hypothesis made in this report that, the session time shows a positive relationship with precision. Next graph 03 shows the different combined precision of the same observation when post processed with a short baseline and long baseline. It also clear that irrelevant of session time always long-baseline shows less precision than the short baseline. Hence these results can generalize to state our hypothesis as there is a negative relationship with baseline length and precision of derived coordinates. However, with increasing observation time this difference can be reduced up to a certain extend.

v.        PROBLEMS ENCOUNTER AND ANOMALIES

It is always expected to have more precision in horizontal coordinates and less precision in vertical, yet TAUO results show in 1, 2, 6, 10, and 20 min observations vertical precision is better than horizontal precision. The elevation of TAUO is the same as the receiver elevation and that might have an effect on vertical precision and hence the vertical precision becomes better than horizontal precision in those observations. 

vi.       RECOMMENDATIONS AND FURTHER INVESTIGATION

If the baseline length close to 100Km it is recommended to carry out a session length of more than 1 hour to get good precision. However, the shorter the baseline gives higher precision.  Further, it is recommended to connect reference stations with the same elevation to obtain better precision

 C.  PRECISION OF BROADCAST EPHEMERIS VS RAPID EPHEMERIS

Satellite-related systematic errors include errors in satellite coordinates (Xe, Ye, Ze) and errors in satellite clock offsets (δte) these are given in an ephemeris. For phase pseudo-range, static double differenced positioning over baseline, either the broadcast ephemeris or a precise ephemeris may be used. GPS constellation system provides broadcast ephemeris real-time and rapid ephemeris within 17-41 hours and will available daily at 1700hrs (UTM). Accuracy of broadcast ephemeris in orbits ~100 cm and satellite clocks SD ~2.5ns whereas rapid ephemeris accuracy in orbits ~3cm and satellite clock SD ~50ps (https://www.igs.org/products). Hence, the coordinates derived from post-process using rapid ephemeris should be precise than the coordinates derived from post-process using broadcast ephemeris. However, GLONASS satellite constellation provides only final ephemeris after 12-18 days.

 i.     HYPOTHESIS   

Rapid ephemeris and broadcast ephemeris has an influence on precision obtained by phase pseudo-range static double differenced positioning over baseline.                                                                                 

ii.     METHODOLOGY

GPS observations session planned for continue 40 hours as given in the study setup and 30-second epoch static observation carried out. The receiver epoch was set to 30 seconds to maintain the same epoch with reference stations in OS Net. The cutoff angle of the receiver was set to 15 degrees to minimize tropospheric refractions and to maintain satellite geometry optimally.

Receiver 2 (Trimble R7) installed in HM school (Antenna at rooftop) collect the data for 40 hours data as time permitted. TBC v 5.30 used to post-process data when using broadcast ephemeris in automatic mode and when processing by rapid ephemeris in precise mode. As indicated in course work setup single baseline design with five different reference stations in OS and details of reference stations and distance as follows,

 iii.      RESULTS

The precision of the derived coordinates was analyzed by the result obtained from post processing of 24 hours static data with all five reference stations using Broadcast ephemeris and rapid ephemeris with a single baseline each.

Same observation and same reference stations were post-processed with rapid ephemeris and result as follows,

To compare the precision and to investigate the relationship between precision and ephemeris used following combined precision of derived coordinates were analyzed.

 Further, weather conditions during all observations in respective areas were obtained, and details as follows. Troposphere delay affects both the code pseudo-range and the phase pseudo-range by equal amounts. The magnitude of this delay is a function of hydrostatic component > 90% (atmospheric pressure, temperature, and elevation angle) and wet component < 5% (distribution of water vapor and elevation angle). Hence, vital weather information for satellite signals are Relative humidity, pressure, and temperature.

 By analyzing weather conditions it is clear the Princes Risborough reference station suffers mostly overcast and high relative humidity compared to other stations and the elevation gain about 120m. Further, consider PHTH and FOST HM had the same conditions as 4km distance.

 iv.      DISCUSSION OF POST PROCESSING AND RESULTS

Results strengthen the arguments made in the previous session as a byproduct of this investigation. Increasing distance (baseline length) gives the low precision in derived coordinates. The final graph (Graph 04) shows there is no significant difference in results obtained by post-processing using broadcast ephemeris and rapid ephemeris in a short baseline. However, mostly the precision of rapid ephemeris shows very closer to broadcast ephemeris and with the long baseline irrelevant of ephemeris used precision decrease as various other factors.

v.       PROBLEMS ENCOUNTER AND ANOMALIES              

In our study, we used broadcast ephemeris and rapid ephemeris downloaded for 24 hours in corresponding observation and applied for post-processing for all five reference stations. Even though we continue observation longer than 24 hours at receiver 2, post-processing done only for the available ephemeris data that was 24 hours. Further, GLONASS satellite constellation rapid ephemeris is not available and only the final ephemeris available after 17-41 days. Hence in our study, only the GPS satellite constellation rapid ephemeris was processed and error indicated as no ephemeris for GLONASS in results. This should not misunderstand as we lost the satellite data but it affects the final precision of derived ordinated. Baseline connecting PHTH, TAUO, and LERI stations show the high precision in broadcast ephemeris than the rapid ephemeris. This is because in the post-processing using broadcast ephemeris TBC work automatic mode and all available satellites used for making observation equation hence to the final result, whereas in post-processing using rapid ephemeris software forced to use rapid ephemeris data only. In this case, only the satellite with rapid ephemeris will be used to form the observation equation. Finally, some of the good satellites from the GLONASS constellation used during post-processing using broadcast ephemeris missing in post processing using rapid ephemeris. This makes the result worst in the later case, hence conclude the low accuracies in post-processing using rapid ephemeris in those baselines.

Post-processed Results show very law precision from baseline connecting Princes Risborough (PRIS 250 Km) reference station. This low combined precision mainly due to vertical precision. It is to be highlighted that the elevation between receiver and reference station PRIS is 124 m and the weather condition in PRIS station might also affect the precision obtained in this study.

vi.        RECOMMENDATIONS AND FURTHER INVESTIGATION                                

It is highly recommended to connect the receiver to a reference station which is having the same or nearly the same elevation. If all the satellites are used in the observation session it is recommended to post-process with final ephemeris than rapid ephemeris which will enable GLONASS constellation to contribute to calculations. However, increasing baseline length reduces the precision even though rapid ephemeris is used. Hence, recommend connecting baseline with short distance to obtain higher accuracy,    

3.    CONCLUSION

GNSS study scheduled to determine how the accuracy of derived coordinates of unknown location (Receiver at HM school) depends on the time duration (T) of the observing session and the distance (D) between the reference station and receiver (Baseline length). However, the final accuracy depends on several other factors in addition to the T and D, including the software used for the processing and methodology adapted in the collection of data and processing. Trimble R7 receiver and TBC Ver. 5.30 used to collect and to process the data and rapid/broadcast ephemeris for respective reference stations were downloaded from Ordnance Survey Network (OS Net). Hence 'static baseline', 'double differenced carrier phase' methodology used in this study.

The paper presented an analysis of the positional accuracy of derived coordinates and five reference stations were used, assuming that those reference stations with optimal observing conditions without any obstructions. Both the receiver at the rooftop also assumed with the optimal condition for satellite signal receiving without multipath errors. However, the geographical situation of HM school masks the horizon from the south which could obstruct satellite signal up to a certain limit. There were a couple of limitations associated with our study. First, because we processed the data with TBC and data collected using GPS dual frequency receiver. For the same reason, our study is incapable of detecting systematic differences between other processing software and other observation technique. Secondly, our study is limited by the fact that it involved GPS data observed during winter, hence seasonal effects (large variation in humidity and temperature) are not sensed. Further long term effect due to large variation in solar activity not sensed however year 2020 shows relatively low solar activity in the cycle. Finally, our study shows longer session length can achieve high precision, and an above 1 hour session period is recommended. Shorter the baseline will give the higher precision and below 100km can give good precision with 1 hour session time. Further, rapid ephemeris gives more precision in the long baseline but not showing significant precision changes with short baseline broadcast ephemeris.